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For a,b,c and d are distnct numbers, if roots of the equation `x^2-10cx-11d=0` are a,b and those of `x^2-10ax-11b=0` are c,d then the value of `a+b+c+d` is

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RESONANCE-EQUATIONS -SELF PRACTICE PROBLEMS:
  1. If alpha, beta are the roots of the quadratic equation cx^2- 2bx + 4a...

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  2. If r be the ratio of the roots of the equation ax^2 + bx + c = 0. show...

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  3. For a,b,c and d are distnct numbers, if roots of the equation x^2-10cx...

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  4. For what values of 'k' the expression (4 - k)x^2 + 2(k + 2)x + 8k +1 w...

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  5. If (x - alpha) be a factor common to a(1)x^(2) + b(1)x +c and a2x^2 +...

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  6. If 3x^(2) + 2alphaxy + 2y^(2) + 2ax - 4y+1 can be resolved into two li...

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  7. Let 4x^2 - 4(alpha - 2)x + alpha - 2 = 0 (alpha in R) be a quadratic e...

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  8. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0, then prove th...

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  9. If ax^2 + 2bx + c = 0 and a1x^2 + 2b(1)x + c(1) = 0 have a common root...

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  10. If 2p^3 - 9pq + 27r = 0 then prove that the roots of the equations rx^...

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  11. If c gt 0 and ax^2 + 2bx + 3c = 0 does not have any real roots then p...

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  12. If f(x) =(x-a) (x-b), then show that f(x) ge (-(a-b)^(2))/4

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  13. Find the least integral value of 'k' for which the quadratic polynomia...

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  14. Find the range of f(x)=(x^2+34 x-71)/(x^3+2x-7)

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  15. Find the interval in which .'m' lies so that the expression (mx^(2) + ...

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  16. Find the value of b for which difference between maximum and minimum v...

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  17. Find all numbers a for each of which the least value of the quadratic ...

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  18. Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then ...

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  19. The value of k for which both the roots of the equation 4x^(2)-20kx+(2...

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  20. Find the values of 'alpha' for which 6 lies between the roots of the e...

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